A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times
type: Item
instance of: scholarly article
title: A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times
zbMATH Open document ID: 1390.90206
DOI: 10.1504/IJMOR.2015.069151
author: Gautam Choudhury
author: Mitali Deka
published in: International Journal of Mathematics in Operational Research
publication date: 2018-06-06T00:00:00Z
review text: Summary: This paper deals with the steady state behaviour of an \(Mx/G/1\) retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with first come, first served (FCFS) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability \(p\) or may serve the next unit, if any, with probability (\(1-p\)). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6881388
zbMATH Keywords: stationary queue size distribution
zbMATH Keywords: random breakdown
zbMATH Keywords: repair time
zbMATH Keywords: retrial times
zbMATH Keywords: Bernoulli vacation
zbMATH Keywords: reliability index
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6881388